Multilevel Physics-Constrained Deep Image Prior Network for Electromagnetic Forward Modeling

Grid size critically influences both computational resource consumption and numerical accuracy in finite difference methods for solving electromagnetic problems. To balance the computational accuracy with resource efficiency, we propose an innovative multilevel physics-constrained deep image prior (ML-PcDIP) network architecture for electromagnetic forward modeling. The ML-PcDIP employs a recursively progressive optimization strategy, leveraging the super-resolution capability of the DIP network. By incorporating physical constraints into the neural network training process, ML-PcDIP facilitates efficient and accurate electromagnetic field predictions. The recursive iterative approach enables precise low-to-high-resolution mapping through stepwise resolution enhancement. Numerical experiments involving scatterers with diverse material properties demonstrate the effectiveness of the method in forward modeling of electromagnetic problems. In addition, practical cases demonstrate that ML-PcDIP substantially reduces reliance on dense mesh input data, significantly lowering computational resource demands. These results demonstrate that the ML-PcDIP network is a promising deep learning method for efficient and accurate electromagnetic forward modeling, providing a feasible solution for large-scale electromagnetic problems.